Condsider the given endothermic reactions. in the table 204 are summarized
Let A denote the event that a reaction final temperature is 271k or less. Let B denote the event that the heat absorbed is above target. determine A. P(A intersection B) B. P(A') C. P(A union B) D. P(A union B') E. P(A' intersection B')

final temp cond. heat absorbed (cal)
below target above target
266k 12 40
271k 44 16
274k 56 36

Step-by-step explanation:

Hello!

Using the information data of 204 endotermic reactions, two events were determined:

A: "the reactions final temperature is 271K or less"

B: "the heat absorbed is above target"

a) P(A∩B) is the intersection between the two events, this means, all the exotermic reaction with final temperature of 271K and less and absorved heat above target:

P(A∩B)= = 0.274

b)P(A∪B) is the probability that the reactions had a final temperature of 271K or are above target, the events A and B are not mutually exclusive, since both can occur at the same time (their intersection isn't void), so you calculate the probability as:

P(A∪B)= P(A) + P(B) - P(A∩B)

To calculate the probability of event A, you have to divide the number of reactions whose final temperature or less by the total number of endotermic reactions, symbolically:

The probability of event B is the quotient between all reactions above target and the total of reactions, symbolically:

Then

P(A∪B)= 0.549 + 0.451 - 0.274= 0.726

c) P(A'∪B')

P(A'∪B')= P(A') + P(B') - P(A'∩B')

If A' is the complementary event of A, meaning all endotermic reactions above a final temperature of 271K, then it's probability is:

P(A')= 1 - P(A)= 1 - 0.549= 0.451

And B' the complementary event of B, this includes all reactions with heat absortion below target, it's probability is:

P(B')= 1 - P(B)= 1 - 0.451= 0.549

And the intersection between both events is:

P(A'∩B')= 56/204= 0.274

Then

P(A'∪B')=0.451 + 0.549 - 0.274= 0.726

d. P(A∪B')

P(A∪B')= P(A) + P(B') - P(A∩B')

P(A∩B') is the intersection of the events "final temperature 271 K or less" and "heat absorbed below target" There are two values that meet these characteristics so the intersection is:

P(A∩B')=

P(A∪B')= 0.549 + 0.549 - 0.274= 0.824

e. P(A'∩B')

P(A'∩B')= 56/204= 0.274

I hope you have a SUPER day!